The “Deflategate” scandal comes to a head in federal court on Monday as lawyers for Patriots quarterback Tom Brady and the NFL commissioner square off one more time before the judge deciding whether to uphold the star’s four-game suspension for underinflated footballs.

That decision could come even as early as Monday, when all parties will be present in the U.S. District Court for the Southern District of New York. Berman has said he will try to rule by Friday, a date agreed upon by the union and the league that would allow the New England Patriots to adjust for Brady’s availability for their Sept.10 season opener.

At earlier hearings, as WSJ reported, Judge Berman grilled both sides throughout the case, while urging them to settle their dispute. At one point, he warned an NFL lawyer that there was precedent for judges to toss out penalties issued by arbitrators.

Legal experts, though, say that despite judge’s stern words, Mr. Brady faces long odds. That’s because courts generally are very reluctant to undo a final, binding arbitration decision, even one they view as seriously flawed.

“It’s an extremely high bar,” said Peter Carfagna, a former outside counsel to the Cleveland Browns who directs Harvard Law School’s sports law clinic.

The Supreme Court made that clear in a 2001 ruling that overturned a lower court that had awarded $3 million to a retired Major League baseball player whose claim had been denied in arbitration.

“Judicial review of a labor-arbitration decision pursuant to such an agreement is very limited,” the Supreme Court wrote in its decision, which said that even if a federal court is convinced an arbitrator made a serious error, that’s not a good enough reason to overrule an arbitrator.

In making the case for why Mr. Brady’s four-game suspension should be vacated, union lawyers representing Mr. Brady have argued that the football commissioner “presided over a fundamentally unfair arbitration process.”

Among their concerns: They say NFL commissioner Roger Goodell should have allowed Mr. Brady to cross-examine NFL general counsel Jeff Pash about his “investigative role” in Deflategate. They also say the commissioner was wrong to deny them access to investigative files, such as notes from witness interviews, used in the report issued by Paul Weiss attorney Ted Wells that formed the basis for the suspension.

Lawyers for Mr. Goodell say none of that justifies throwing out the suspension.

Courts have said that an arbitrator must grant parties a “fundamentally fair hearing.” But that standard has been interpreted to mean meeting “minimal requirements of fairness.”

Mr. Carfagna told Law Blog that the players’ union “has done a great job of making every conceivable argument they could make,” what he called the “smorgasbord approach.” But he said many of Mr. Brady’s arguments attack a process that NFL players agreed to in their collective bargaining agreement with owners.

He said Judge Berman could give Mr. Brady a partial victory by requiring the commissioner to redo parts of the arbitration proceedings without entirely jettisoning Mr. Goodell’s decision.

USA Today also notes that whatever Judge Berman decides, the losing party will likely ask the Second U.S. Circuit Court of Appeals to review it.

If the suspension is upheld, Judge Berman or a higher court could also stay the ruling while the appeals process plays out, allowing Mr. Brady to start the season.